Allegations baby Asha was deliberately harmed by her mother as a way to get the family off Nauru and into Australia have been refuted by medical records and dismissed by police and advocates.

The suggestion that the Nepalese woman deliberately harmed her one-year-old child appeared to have grown from comments made by the immigration minister, Peter Dutton, in parliament, a subsequent attempt by crossbenchers to censure him and media reports on Tuesday of a police investigation.

The Queensland police investigation, sparked by a child protection notification reportedly from a guard, has since been closed and no charges have been laid.

On Monday Dutton suggested the government was the target of attempted blackmail by asylum seekers seeking healthcare.

Dutton had been asked a question in parliament referencing baby Asha and, within his answer, was the following statement: “I’m not going to conduct a situation, not going to preside over a situation where we have people self-harming to come to hospitals in this country because they believe that is the route out into the Australian community for Australian citizenship.”

He immediately followed the statement with comments about baby Asha, prompting accusations he was implying Asha had been deliberately harmed by her mother.

The Tasmanian MP Andrew Wilkie moved to censure Dutton for his comments, telling parliament the accusation that people self-harmed to gain citizenship was “one of the ugliest things I have heard in this place in my time serving here”.

The motion was seconded by the Greens MP Adam Bandt and supported by the independent MP Cathy McGowan. However, it was defeated when Labor voted with the Coalition because, Labor’s immigration spokesman, Richard Marles, said, Dutton’s comments had been “over egged” by Wilkie.

Dutton defended his comments and said he made no judgment about Asha’s injuries.

On Tuesday the Courier Mail reported a guard had alleged Asha’s mother had “confessed” to purposefully harming Asha to get them out of Nauru.

It is not known exactly what, if any, statement made by Asha’s mother – who speaks English as a second language – led to the actioning of a child protection notification by the guard.

Queensland police confirmed to Guardian Australia it had received a child protection notification but would not say when it was received. The spokeswoman said an investigation was conducted and finalised.

An asylum seeker advocate, Natasha Blucher, said Asha’s mother had been interviewed by police last week. Blucher, a former Save the Children worker who had been cleared of accusations she and others incited asylum seekers to self-harm, said the questions largely centred around whether Blucher had coached her to burn Asha.

Blucher was not subsequently questioned and the investigation has since closed.

Blucher, who has known Asha’s parents for about two years, said Asha’s mother would be “absolutely distraught” at the suggestion she had harmed her daughter.

“If anything, she has been very protective of the child in a difficult environment,” Blucher said. “She’s done everything she possibly can to keep her safe.”

Hospital records of Asha’s treatment, seen by Guardian Australia, show there was no evidence anybody else was involved in her injury.

Asha, who is a year old, sustained a “superficial, partial thickness” burn to her chest in an accident with recently boiled water that was cooling in the tent in which she lived.

“The injury occurred when [Asha] pulled a bowl containing recently boiled water off a table onto herself,” the medical record said. “[Asha] lives in a tent with no kitchen facilities except for a kettle. [Asha’s] mother boils all the water she consumes to ensure it is safe for drinking.

“There is no clinical evidence that the burn injury was non-accidental.”

Daniel Webb, who is acting for the family, said the government needed to get perspective on the issue.

“Last night was this family’s first night of freedom in two-and-a-half years,” he said. “It’s incredibly sad that they have to wake up to such hurtful things being said about them. Asha’s mother will be really confused and upset.”

“Dutton is in possession of medical reports which clearly state Baby Asha’s injuries were accidental,” Narayanasamy said.

“It’s rotten politics and we will ensure the family is able to fully explore their defamation options against this minister and his Border Force.”

Dutton had since repeated his question time comments, telling Channel Nine: “We are not going to allow people smugglers to get out a message that if you seek assistance in an Australian hospital, that somehow that is your formula to becoming an Australian citizen.”

At the time – which was shortly before a federal election the Coalition would go on to win – ministers in the Howard government insisted that asylum seekers arriving in Australian waters by boat had deliberately thrown their children into the sea in a “planned and premeditated” attempt to force the navy to take them to Australia.

The defence minister at the time, Peter Reith, released photographs of children in the sea wearing life jackets, asserting the pictures were evidence the government’s stated version of events was “absolute fact”.

The then prime minister, John Howard, said: “I express my anger at the behaviour of those people and I repeat it: I can’t comprehend how genuine refugees would throw their children overboard … I certainly don’t want people of that type in Australia, I really don’t.”

It was found by a subsequent parliamentary inquiry that the version of events presented by the government was untrue: that no children were thrown into the water in the incident; that the pictures presented were taken a day after the alleged incident was said to have taken place (when the asylum seeker boat broke up and sank under tow from the navy and almost all passengers ended up in the water); and that military chiefs had explicitly told government officials no children were thrown overboard in the incident.

The Greens senator Sarah Hanson Young said the government had “form” when it came to making false accusations and allusions.

“The children overboard affair and the recent unfair sacking of 10 Save the Children workers on Nauru shows why we should be suspicious of what this government says,” she said. “When it comes to who to trust out of Peter Dutton or the medical professionals who are trying to protect children on Nauru, I know who I’ll back every time.”

Dutton’s office has been contacted for comment.

Asha and her family are still on the Australian mainland, according to the department of immigration, but their exact location since being moved into community detention is unknown. Dutton has said that once “legal and medical” issues are resolved, all families will be returned to Nauru. Lawyers and advocates said they had been unable to contact the family for up to three days, before making contact Monday night.